Harmonic measure is absolutely continuous with respect to the Hausdorff measure on all low-dimensional uniformly rectifiable sets
G David, S Mayboroda - International Mathematics Research …, 2023 - academic.oup.com
Spectacular achievements of the past 20 years at the interface of harmonic analysis,
geometric measure theory, and partial diffferential equations (PDEs) have finally identified …
geometric measure theory, and partial diffferential equations (PDEs) have finally identified …
Elliptic theory in domains with boundaries of mixed dimension
G David, J Feneuil, S Mayboroda - arXiv preprint arXiv:2003.09037, 2020 - arxiv.org
Take an open domain $\Omega\subset\mathbb R^ n $ whose boundary may be composed
of pieces of different dimensions. For instance, $\Omega $ can be a ball on $\mathbb R^ 3 …
of pieces of different dimensions. For instance, $\Omega $ can be a ball on $\mathbb R^ 3 …
Absolute continuity of the harmonic measure on low dimensional rectifiable sets
J Feneuil - The Journal of Geometric Analysis, 2022 - Springer
In the past decades, we learnt that uniform rectifiability is often a right candidate to go past
Lipschitz boundaries in boundary value problems. If Ω is an open domain in R n with mild …
Lipschitz boundaries in boundary value problems. If Ω is an open domain in R n with mild …
On the condition for elliptic operators in 1-sided nontangentially accessible domains satisfying the capacity density condition
M Cao, Ó Domínguez, JM Martell… - Forum of Mathematics …, 2022 - cambridge.org
Let,, be a-sided nontangentially accessible domain, that is, a set which is quantitatively open
and path-connected. Assume also that satisfies the capacity density condition. Let, be two …
and path-connected. Assume also that satisfies the capacity density condition. Let, be two …
[图书][B] Rectifiability: a survey
P Mattila - 2023 - books.google.com
Rectifiable sets, measures, currents and varifolds are foundational concepts in geometric
measure theory. The last four decades have seen the emergence of a wealth of connections …
measure theory. The last four decades have seen the emergence of a wealth of connections …
Carleson perturbations of elliptic operators on domains with low dimensional boundaries
S Mayboroda, B Poggi - Journal of Functional Analysis, 2021 - Elsevier
We prove an analogue of a perturbation result for the Dirichlet problem of divergence form
elliptic operators by Fefferman, Kenig and Pipher, for the degenerate elliptic operators of …
elliptic operators by Fefferman, Kenig and Pipher, for the degenerate elliptic operators of …
Green functions and smooth distances
J Feneuil, L Li, S Mayboroda - Mathematische Annalen, 2024 - Springer
In the present paper, we show that for an optimal class of elliptic operators with non-smooth
coefficients on a 1-sided Chord-Arc domain, the boundary of the domain is uniformly …
coefficients on a 1-sided Chord-Arc domain, the boundary of the domain is uniformly …
Approximation of Green functions and domains with uniformly rectifiable boundaries of all dimensions
G David, S Mayboroda - Advances in Mathematics, 2022 - Elsevier
The present paper concerns divergence form elliptic and degenerate elliptic operators in a
domain Ω⊂ R n, and establishes the equivalence between the uniform rectifiability of the …
domain Ω⊂ R n, and establishes the equivalence between the uniform rectifiability of the …
Rectifiability; a survey
P Mattila - arXiv preprint arXiv:2112.00540, 2021 - arxiv.org
arXiv:2112.00540v3 [math.CA] 1 Mar 2022 Page 1 arXiv:2112.00540v3 [math.CA] 1 Mar
2022 RECTIFIABILITY; A SURVEY PERTTI MATTILA Abstract. This is a survey on …
2022 RECTIFIABILITY; A SURVEY PERTTI MATTILA Abstract. This is a survey on …
Branch points for (almost-) minimizers of two-phase free boundary problems
We study the existence and structure of branch points in two-phase free boundary problems.
More precisely, we construct a family of minimizers to an Alt–Caffarelli–Friedman-type …
More precisely, we construct a family of minimizers to an Alt–Caffarelli–Friedman-type …